Finite Group Databasebeta

← #31805440

Subgroups — #31805440

Order 17792.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581534C211yesmaximal, characteristic
2#22581271C212yesmaximal, complemented
3#22580686C212yesmaximal, complemented
4#22580679C211yesmaximal, characteristic, complemented
5#400×C139C211yesmaximal, characteristic, complemented
6C2×#14555785—21no—
7#17984822—22no—
8#17984817—22no—
9#17984816—21no—
10#17984816C2212yes—
11#17984773—22no—
12#17984762—22no—
13C22⋊(C139⋊C8)C2212yes—
14C2×C4⋊C4×C139C2211yescharacteristic
15C2×C4⋊C4×C139C2211yescharacteristic
16#95×C139—21no—
17#95×C139—21no—
18#95×C139C2211yescharacteristic
19#14555785—42no—
20#14555785—42no—
21C2×Dic278—21no—
22C2×D556—21no—
23C2×D556—21no—
24C2×D556D412yes—
25C2×C22⋊D139—22no—
26C2×C4×D139—22no—
27C2×C139⋊C8—22no—
28C4⋊Dic139—21no—
29C4⋊Dic139D412yes—
30(C2×D139)⋊C4—22no—
31(C2×D139)⋊C4—22no—
32C22×C4×C139—21no—
33C22×C4×C139—21no—
34C22×C4×C139D411yescharacteristic
35C22×C4×C139D411yescharacteristic
36C22×C4×C139C2311yescharacteristic
37C4⋊C4×C139—22no—
38C4⋊C4×C139—22no—
39C22×D139—22no—
40Dic278—42no—
41D556—42no—
42D556—42no—
43D556—81no—
44C22⋊D139—42no—
45C22⋊D139—42no—
46C2×Dic139—22no—
47C4×D139—44no—
48C139⋊C8—42no—
49C23×C139C2×D411yescharacteristic
50C2×C4×C139—21no—
51C2×C4×C139—21no—
52C2×C4×C139—21no—
53C2×C4×C139—41no—
54C2×C4×C139—41no—
55C2×C4×C139—41no—
56C2×C4×C139—41no—
57C2×C4×C139—42no—
58C2×C4×C139—41no—
59C2×C4×C139—41no—
60C2×C4×C139SD1612yes—
61C2×C4×C139C2×D412yes—
62C22×C139—21no—
63C22×C139—21no—
64C22×C139#12011yescharacteristic
65C22×C139C2×SD1611yescharacteristic
66C22×C139AGL(1,ℤ/8)11yescharacteristic
67C2×D139—42no—
68C2×D139—42no—
69C2×D139—42no—
70C4×C139—22no—
71C4×C139—22no—
72C4×C139—41no—
73C4×C139—81no—
74C4×C139—81no—
75Dic139—42no—
76C2×C139—21no—
77C2×C139—21no—
78C2×C139#45011yescharacteristic
79C2×C139#45411yescharacteristic
80C2×C139#45811yescharacteristic
81D139—82no—
82C139#161611yescharacteristic, complemented, Sylow
83#1616—1391nomaximal, Sylow
84#537—1391no—
85#481—1392no—
86#400D13911yescharacteristic, complemented
87#327—1392no—
88#324—1391no—
89C2×#41—2781no—
90C22⋊Q8—2782no—
91#121—2782no—
92#121—2781no—
93#121—1392no—
94C2×C4⋊C4C2×D13911yescharacteristic
95C2×C4⋊C4C2×D13911yescharacteristic
96#106—2782no—
97#102—2782no—
98C22⋊C8—1392no—
99#95—21no—
100#95—21no—
101#95C2×D13911yescharacteristic
102#41—5562no—
103#41—5562no—
104C2×Q8—2781no—
105C2×D4—2781no—
106C2×D4—2781no—
107C2×D4—2782no—
108C2×D4—1392no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—2782no—
112C22×C4C22⋊D13911yescharacteristic
113C22×C4C22⋊D13911yescharacteristic
114C22×C4C22×D13911yescharacteristic
115C2×C8—2782no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—2781no—
119C4⋊C4—1392no—
120C22⋊C4—2782no—
121C22⋊C4—2782no—
122C23—2782no—
123C23C2×C22⋊D13911yescharacteristic
124Q8—5562no—
125D4—5562no—
126D4—5562no—
127D4—5562no—
128D4—5562no—
129D4—11121no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—2782no—
141C2×C4—5564no—
142C2×C4#1455577212yes—
143C2×C4D4×D13912yes—
144C8—5562no—
145C22—21no—
146C22—21no—
147C22—5562no—
148C22—5562no—
149C22—5562no—
150C22#1798481011yescharacteristic
151C22C2×#1455577211yescharacteristic
152C22#1798486711yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—5562no—
159C2—21no—
160C2—21no—
161C2—11122no—
162C2#2258110311yescharacteristic
163C2#2258112511yescharacteristic
164C2#2258114211yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#400×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#400D139
hypocenterC139#1616
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22581271C2semidirect
3. #22580686C2semidirect
4. #22580679C2semidirect
5. #400×C139C2semidirect
82. C139#1616semidirect
86. #400D139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225815342
#225812712
#225806862
#225806792
#400×C1392
#1616139